To date, almost all experimental evaluations of machine learning-based recognition algorithms in computer vision have taken the form of "closed set" recognition, whereby all testing classes are known at training time. A more realistic scenario for vision applications is "open set" recognition, where incomplete knowledge of the world is present at training time, and unknown classes can be submitted to an algorithm during testing. This paper explores the nature of open set recognition and formalizes its definition as a constrained minimization problem. The open set recognition problem is not well addressed by existing algorithms because it requires strong generalization. As a step toward a solution, we introduce a novel "1-vs-set machine," which sculpts a decision space from the marginal distances of a 1-class or binary SVM with a linear kernel. This methodology applies to several different applications in computer vision where open set recognition is a challenging problem, including object recognition and face verification. We consider both in this work, with large scale cross-dataset experiments performed over the Caltech 256 and ImageNet sets, as well as face matching experiments performed over the Labeled Faces in the Wild set. The experiments highlight the effectiveness of machines adapted for open set evaluation compared to existing 1-class and binary SVMs for the same tasks.